Write simple expressions that record calculations with numbers, and
interpret numerical expressions without evaluating them. For example,
express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 +
7). Recognize that 3 × (18932 + 921) is three times as large as 18932 +
921, without having to calculate the indicated sum or product.

Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Lessons

5.NBT.6

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Lessons

5.NF.3

Interpret a fraction as division of the numerator by
the denominator (a/b = a ÷ b). Solve word problems involving division of
whole numbers leading to answers in the form of fractions or mixed
numbers, e.g., by using visual fraction models or equations to represent
the problem. For example, interpret 3/4 as the result of dividing 3 by
4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are
shared equally among 4 people each person has a share of size 3/4. If 9
people want to share a 50-pound sack of rice equally by weight, how many
pounds of rice should each person get? Between what two whole numbers
does your answer lie?

5.NF.4.a Interpret the product
(a/b) × q as a parts of a partition of q into b equal parts;
equivalently, as the result of a sequence of operations a × q ÷ b. For
example, use a visual fraction model to show (2/3) × 4 = 8/3, and create
a story context for this equation. Do the same with (2/3) × (4/5) =
8/15. (In general, (a/b) × (c/d) = ac/bd.)

5.NF.4.b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

5.NF.5.b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

5.NF.7.a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

5.NF.7.b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

5.NF.7.c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

Classify two-dimensional figures into categories based on their properties

Lessons

5G.3

Understand that attributes belonging to a category of two-dimensional
figures also belong to all subcategories of that category. For example,
all rectangles have four right angles and squares are rectangles, so all
squares have four right angles.